Quotation taken from the book “Jesus, The Apostles And The Early Church” by Joseph Ratzinger (Pope Benedict XVI), pages 47 - 48, published by Ignatius Press, copyright 2007:

"At the time of Jesus’ Passion and death, Peter had betrayed him by denying him three times, a betrayal he almost immediately regretted, weeping bitterly over what he had done. After his weeping he was finally ready for the mission for which Jesus had been preparing him.

"On a spring morning, this mission will be entrusted to him by the Risen Christ. The encounter takes place on the shore of the Lake of Tiberias. John the Evangelist recounts the conversation between Jesus and Peter in that circumstance. There is a very significant play on words.

"In Greek, the word fileo means the love of friendship, tender but not all-encompassing; instead, the word agapao means love without reserve, total and unconditional. Jesus asks Peter the first time: 'Simon . . . do you love me (agapas-me)' with this total and unconditional love (Jn 21:15)?

"Prior to the experience of betrayal, the Apostle certainly would have said: 'I love you (agapo-se) unconditionally.' Now that he has known the bitter sadness of infidelity, the drama of his own weakness, he says with humility: “Lord; you know that I love you (filo-se)”, that is, 'I love you with my poor human love.' Christ insists: 'Simon, do you love me with this total love that I want?' And Peter repeats the response of his humble human love: 'Kyrie, filo-se', 'Lord, I love you as I am able to love you.' The third time Jesus only says to Simon: 'Fileis-me?”, “Do you love me?'

"Simon understands that his poor love is enough for Jesus, it is the only one of which he is capable; nonetheless he is grieved that the Lord spoke to him in this way. He thus replies: 'Lord, you know everything; you know that I love you (filo-se).'

"This is to say that Jesus has put himself on the level of Peter, rather than Peter on Jesus’ level! It is exactly this divine conformity that gives hope to the Disciple, who experienced the pain of infidelity.

"From here is born the trust that makes him able to follow [Christ] to the end: “This he said to show by what death he was to glorify God. And after this he said to him, ‘Follow me’ (Jn 21:19).

"From that day, Peter 'followed' the Master with the precise awareness of his own fragility; but this understanding did not discourage him. Indeed, he knew that he could count on the presence of the Risen One beside him."

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My related thought: I think Ratzinger’s (Pope Benedict's) explication of John 21 is helpful in understanding some language in John’s First Epistle.

John wrote:

"He who says that he knows [God], and does not keep his commandments, is a liar and the truth is not in him. But he who keeps his word, in him the love of God is truly perfected; and by this we know that we are in him. He who says that he abides in him, ought himself also to walk just as he walked.

"Beloved, no new commandment am I writing to you, but an old commandment, which you had from the beginning. The old commandment is the word you have heard. Again, a new commandment I am writing to you, and this is true both in him and in you. Because the darkness has passed away and the true light is now shining. He who says that he is in the light, and hates his brother, is in the darkness still. He who loves his brother abides in the light, and for him there is no stumbling" (1 Jn 1:4 - 10).

I think John is saying that if we keep God’s commandments, this is a sign that we love and we can be sure that we are in God. This is the “old commandment” to which John referred. But John also gives us the same “new commandment” that Jesus had given us: “A new commandment,” Jesus said, “I give you, that you love one another; that as I have loved you, you also love one another” (Jn 13:34). This is the dramatically higher standard of agapao—to love one another as Jesus has loved us, ready when necessary even to lay down his life for his friends (Jn 15:12 - 17). Insofar as the old commandment demanded love of God, it was already that high: “you shall love the Lord, your God, with all your heart, and with all your soul, and with all your strength” (Deut 6:5). But insofar as it concerned loving one another, it had not been so high: “Take no revenge against your fellow countrymen,” it commanded; “You shall love your neighbor as yourself” (Lev 19:188). The Old Testament command to love your neighbor thus only applied to one’s fellow countrymen, and even as to them it seems to have been satisfied if one merely took no revenge. This left them free to hate their enemies (Mt 19:43) which in practice included most Gentiles. Now Jesus raised the bar.

Despite this daunting new commandment, Jesus’ exchange with Peter reassures us that he is prepared to condescend to our weakness if we find it beyond our ability to love him so perfectly; and Jesus’ command to “feed his sheep” for love of him implies that he will also accept Peter’s performance in regard to his sheep if Peter sincerely tries (Jn 21:15 - 17). We, like Peter, are supposed to try, but if we fail it is no reason to get depressed or discouraged. We simply must keep doing the best we can, and love as we are able. Jesus will accept whatever love we are able to give to him and to his sheep: “Beloved, let us love one another, for love is from God. And everyone who loves is born of God, and knows God. He who does not love does not know God; for God is love” (1 Jn 4:7 - 88). John in his Epistle does not insist that a particular degree of love is required. The highest level is only an aspirational goal, but we are commanded that we must truly aspire to it.